1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 455,969 x 11
##    site_type date       sex    age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr>  <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 female miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 female miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 female 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 female 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 female 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 female 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 female 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 female 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 female 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 female 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 455,959 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     63
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      5
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      8
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      1
## 144   2020-07-22          East of England      2
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      1
## 150   2020-07-28          East of England      2
## 151   2020-07-29          East of England      0
## 152   2020-07-30          East of England      0
## 153   2020-07-31          East of England      1
## 154   2020-08-01          East of England      0
## 155   2020-08-02          East of England      0
## 156   2020-08-03          East of England      0
## 157   2020-08-04          East of England      1
## 158   2020-08-05          East of England      1
## 159   2020-08-06          East of England      0
## 160   2020-08-07          East of England      1
## 161   2020-08-08          East of England      0
## 162   2020-08-09          East of England      0
## 163   2020-08-10          East of England      1
## 164   2020-08-11          East of England      2
## 165   2020-08-12          East of England      1
## 166   2020-08-13          East of England      0
## 167   2020-08-14          East of England      1
## 168   2020-08-15          East of England      1
## 169   2020-08-16          East of England      0
## 170   2020-08-17          East of England      0
## 171   2020-08-18          East of England      2
## 172   2020-08-19          East of England      1
## 173   2020-08-20          East of England      1
## 174   2020-08-21          East of England      0
## 175   2020-08-22          East of England      1
## 176   2020-08-23          East of England      1
## 177   2020-08-24          East of England      0
## 178   2020-08-25          East of England      0
## 179   2020-08-26          East of England      1
## 180   2020-08-27          East of England      1
## 181   2020-08-28          East of England      0
## 182   2020-08-29          East of England      0
## 183   2020-08-30          East of England      0
## 184   2020-08-31          East of England      0
## 185   2020-09-01          East of England      0
## 186   2020-09-02          East of England      0
## 187   2020-09-03          East of England      1
## 188   2020-09-04          East of England      1
## 189   2020-09-05          East of England      0
## 190   2020-09-06          East of England      1
## 191   2020-09-07          East of England      0
## 192   2020-09-08          East of England      0
## 193   2020-09-09          East of England      0
## 194   2020-09-10          East of England      0
## 195   2020-09-11          East of England      0
## 196   2020-09-12          East of England      0
## 197   2020-09-13          East of England      1
## 198   2020-09-14          East of England      1
## 199   2020-09-15          East of England      0
## 200   2020-09-16          East of England      0
## 201   2020-09-17          East of England      0
## 202   2020-09-18          East of England      0
## 203   2020-09-19          East of England      0
## 204   2020-09-20          East of England      2
## 205   2020-09-21          East of England      0
## 206   2020-09-22          East of England      2
## 207   2020-09-23          East of England      1
## 208   2020-09-24          East of England      0
## 209   2020-09-25          East of England      1
## 210   2020-09-26          East of England      1
## 211   2020-09-27          East of England      1
## 212   2020-09-28          East of England      2
## 213   2020-09-29          East of England      2
## 214   2020-09-30          East of England      2
## 215   2020-10-01          East of England      2
## 216   2020-10-02          East of England      1
## 217   2020-10-03          East of England      1
## 218   2020-10-04          East of England      0
## 219   2020-10-05          East of England      0
## 220   2020-10-06          East of England      4
## 221   2020-10-07          East of England      6
## 222   2020-10-08          East of England      3
## 223   2020-10-09          East of England      1
## 224   2020-10-10          East of England      6
## 225   2020-10-11          East of England      2
## 226   2020-10-12          East of England      2
## 227   2020-10-13          East of England      1
## 228   2020-10-14          East of England      3
## 229   2020-10-15          East of England      4
## 230   2020-10-16          East of England      5
## 231   2020-10-17          East of England      6
## 232   2020-10-18          East of England      7
## 233   2020-10-19          East of England      5
## 234   2020-10-20          East of England      9
## 235   2020-10-21          East of England      8
## 236   2020-10-22          East of England      7
## 237   2020-10-23          East of England     14
## 238   2020-10-24          East of England      1
## 239   2020-10-25          East of England     10
## 240   2020-10-26          East of England     10
## 241   2020-10-27          East of England      8
## 242   2020-10-28          East of England     12
## 243   2020-10-29          East of England     10
## 244   2020-10-30          East of England     12
## 245   2020-10-31          East of England     15
## 246   2020-11-01          East of England     14
## 247   2020-11-02          East of England      9
## 248   2020-11-03          East of England     14
## 249   2020-11-04          East of England     11
## 250   2020-11-05          East of England     12
## 251   2020-11-06          East of England     18
## 252   2020-11-07          East of England     10
## 253   2020-11-08          East of England     13
## 254   2020-11-09          East of England     16
## 255   2020-11-10          East of England     26
## 256   2020-11-11          East of England     14
## 257   2020-11-12          East of England     14
## 258   2020-11-13          East of England     21
## 259   2020-11-14          East of England     19
## 260   2020-11-15          East of England     13
## 261   2020-11-16          East of England     11
## 262   2020-11-17          East of England     17
## 263   2020-11-18          East of England     19
## 264   2020-11-19          East of England     23
## 265   2020-11-20          East of England     24
## 266   2020-11-21          East of England     19
## 267   2020-11-22          East of England     21
## 268   2020-11-23          East of England     18
## 269   2020-11-24          East of England     21
## 270   2020-11-25          East of England     19
## 271   2020-11-26          East of England     19
## 272   2020-11-27          East of England     14
## 273   2020-11-28          East of England     28
## 274   2020-11-29          East of England     19
## 275   2020-11-30          East of England     22
## 276   2020-12-01          East of England     26
## 277   2020-12-02          East of England     18
## 278   2020-12-03          East of England     24
## 279   2020-12-04          East of England     25
## 280   2020-12-05          East of England     25
## 281   2020-12-06          East of England     21
## 282   2020-12-07          East of England     16
## 283   2020-12-08          East of England     26
## 284   2020-12-09          East of England     20
## 285   2020-12-10          East of England     32
## 286   2020-12-11          East of England     32
## 287   2020-12-12          East of England     27
## 288   2020-12-13          East of England     25
## 289   2020-12-14          East of England     32
## 290   2020-12-15          East of England     35
## 291   2020-12-16          East of England     29
## 292   2020-12-17          East of England     42
## 293   2020-12-18          East of England     44
## 294   2020-12-19          East of England     54
## 295   2020-12-20          East of England     52
## 296   2020-12-21          East of England     66
## 297   2020-12-22          East of England     52
## 298   2020-12-23          East of England     62
## 299   2020-12-24          East of England     61
## 300   2020-12-25          East of England     58
## 301   2020-12-26          East of England     64
## 302   2020-12-27          East of England     54
## 303   2020-12-28          East of England     71
## 304   2020-12-29          East of England     54
## 305   2020-12-30          East of England     76
## 306   2020-12-31          East of England     82
## 307   2021-01-01          East of England     89
## 308   2021-01-02          East of England     66
## 309   2021-01-03          East of England     78
## 310   2021-01-04          East of England     87
## 311   2021-01-05          East of England    102
## 312   2021-01-06          East of England    100
## 313   2021-01-07          East of England    116
## 314   2021-01-08          East of England     96
## 315   2021-01-09          East of England    133
## 316   2021-01-10          East of England    125
## 317   2021-01-11          East of England    126
## 318   2021-01-12          East of England    131
## 319   2021-01-13          East of England    131
## 320   2021-01-14          East of England    126
## 321   2021-01-15          East of England    118
## 322   2021-01-16          East of England    131
## 323   2021-01-17          East of England    133
## 324   2021-01-18          East of England    120
## 325   2021-01-19          East of England    129
## 326   2021-01-20          East of England    147
## 327   2021-01-21          East of England    135
## 328   2021-01-22          East of England    122
## 329   2021-01-23          East of England    102
## 330   2021-01-24          East of England    101
## 331   2021-01-25          East of England    112
## 332   2021-01-26          East of England     89
## 333   2021-01-27          East of England     94
## 334   2021-01-28          East of England    110
## 335   2021-01-29          East of England     95
## 336   2021-01-30          East of England     85
## 337   2021-01-31          East of England     73
## 338   2021-02-01          East of England     65
## 339   2021-02-02          East of England     74
## 340   2021-02-03          East of England     82
## 341   2021-02-04          East of England     75
## 342   2021-02-05          East of England     66
## 343   2021-02-06          East of England     77
## 344   2021-02-07          East of England     62
## 345   2021-02-08          East of England     73
## 346   2021-02-09          East of England     62
## 347   2021-02-10          East of England     52
## 348   2021-02-11          East of England     52
## 349   2021-02-12          East of England     47
## 350   2021-02-13          East of England     47
## 351   2021-02-14          East of England     32
## 352   2021-02-15          East of England     48
## 353   2021-02-16          East of England     45
## 354   2021-02-17          East of England     46
## 355   2021-02-18          East of England     29
## 356   2021-02-19          East of England     28
## 357   2021-02-20          East of England     30
## 358   2021-02-21          East of England     24
## 359   2021-02-22          East of England     26
## 360   2021-02-23          East of England     27
## 361   2021-02-24          East of England     17
## 362   2021-02-25          East of England     23
## 363   2021-02-26          East of England     15
## 364   2021-02-27          East of England     23
## 365   2021-02-28          East of England     15
## 366   2021-03-01          East of England     17
## 367   2021-03-02          East of England     14
## 368   2021-03-03          East of England      2
## 369   2020-03-01                   London      0
## 370   2020-03-02                   London      0
## 371   2020-03-03                   London      0
## 372   2020-03-04                   London      0
## 373   2020-03-05                   London      0
## 374   2020-03-06                   London      1
## 375   2020-03-07                   London      0
## 376   2020-03-08                   London      0
## 377   2020-03-09                   London      1
## 378   2020-03-10                   London      0
## 379   2020-03-11                   London      5
## 380   2020-03-12                   London      6
## 381   2020-03-13                   London     10
## 382   2020-03-14                   London     13
## 383   2020-03-15                   London      9
## 384   2020-03-16                   London     15
## 385   2020-03-17                   London     23
## 386   2020-03-18                   London     28
## 387   2020-03-19                   London     25
## 388   2020-03-20                   London     44
## 389   2020-03-21                   London     49
## 390   2020-03-22                   London     54
## 391   2020-03-23                   London     63
## 392   2020-03-24                   London     86
## 393   2020-03-25                   London    112
## 394   2020-03-26                   London    130
## 395   2020-03-27                   London    130
## 396   2020-03-28                   London    123
## 397   2020-03-29                   London    145
## 398   2020-03-30                   London    151
## 399   2020-03-31                   London    183
## 400   2020-04-01                   London    202
## 401   2020-04-02                   London    191
## 402   2020-04-03                   London    199
## 403   2020-04-04                   London    231
## 404   2020-04-05                   London    195
## 405   2020-04-06                   London    198
## 406   2020-04-07                   London    220
## 407   2020-04-08                   London    239
## 408   2020-04-09                   London    207
## 409   2020-04-10                   London    171
## 410   2020-04-11                   London    178
## 411   2020-04-12                   London    159
## 412   2020-04-13                   London    166
## 413   2020-04-14                   London    143
## 414   2020-04-15                   London    143
## 415   2020-04-16                   London    140
## 416   2020-04-17                   London    101
## 417   2020-04-18                   London    101
## 418   2020-04-19                   London    104
## 419   2020-04-20                   London     96
## 420   2020-04-21                   London     96
## 421   2020-04-22                   London    109
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## 423   2020-04-24                   London     71
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## 1446  2021-02-05 North East and Yorkshire     77
## 1447  2021-02-06 North East and Yorkshire     52
## 1448  2021-02-07 North East and Yorkshire     56
## 1449  2021-02-08 North East and Yorkshire     51
## 1450  2021-02-09 North East and Yorkshire     52
## 1451  2021-02-10 North East and Yorkshire     62
## 1452  2021-02-11 North East and Yorkshire     62
## 1453  2021-02-12 North East and Yorkshire     57
## 1454  2021-02-13 North East and Yorkshire     52
## 1455  2021-02-14 North East and Yorkshire     58
## 1456  2021-02-15 North East and Yorkshire     58
## 1457  2021-02-16 North East and Yorkshire     42
## 1458  2021-02-17 North East and Yorkshire     47
## 1459  2021-02-18 North East and Yorkshire     41
## 1460  2021-02-19 North East and Yorkshire     42
## 1461  2021-02-20 North East and Yorkshire     36
## 1462  2021-02-21 North East and Yorkshire     38
## 1463  2021-02-22 North East and Yorkshire     20
## 1464  2021-02-23 North East and Yorkshire     36
## 1465  2021-02-24 North East and Yorkshire     31
## 1466  2021-02-25 North East and Yorkshire     26
## 1467  2021-02-26 North East and Yorkshire     25
## 1468  2021-02-27 North East and Yorkshire     32
## 1469  2021-02-28 North East and Yorkshire     27
## 1470  2021-03-01 North East and Yorkshire     18
## 1471  2021-03-02 North East and Yorkshire     12
## 1472  2021-03-03 North East and Yorkshire      3
## 1473  2020-03-01               North West      0
## 1474  2020-03-02               North West      0
## 1475  2020-03-03               North West      0
## 1476  2020-03-04               North West      0
## 1477  2020-03-05               North West      1
## 1478  2020-03-06               North West      0
## 1479  2020-03-07               North West      0
## 1480  2020-03-08               North West      1
## 1481  2020-03-09               North West      0
## 1482  2020-03-10               North West      0
## 1483  2020-03-11               North West      0
## 1484  2020-03-12               North West      2
## 1485  2020-03-13               North West      3
## 1486  2020-03-14               North West      1
## 1487  2020-03-15               North West      4
## 1488  2020-03-16               North West      2
## 1489  2020-03-17               North West      4
## 1490  2020-03-18               North West      6
## 1491  2020-03-19               North West      7
## 1492  2020-03-20               North West     10
## 1493  2020-03-21               North West     11
## 1494  2020-03-22               North West     13
## 1495  2020-03-23               North West     15
## 1496  2020-03-24               North West     21
## 1497  2020-03-25               North West     21
## 1498  2020-03-26               North West     29
## 1499  2020-03-27               North West     36
## 1500  2020-03-28               North West     28
## 1501  2020-03-29               North West     46
## 1502  2020-03-30               North West     67
## 1503  2020-03-31               North West     52
## 1504  2020-04-01               North West     86
## 1505  2020-04-02               North West     96
## 1506  2020-04-03               North West     95
## 1507  2020-04-04               North West     98
## 1508  2020-04-05               North West    102
## 1509  2020-04-06               North West    100
## 1510  2020-04-07               North West    136
## 1511  2020-04-08               North West    127
## 1512  2020-04-09               North West    119
## 1513  2020-04-10               North West    117
## 1514  2020-04-11               North West    138
## 1515  2020-04-12               North West    125
## 1516  2020-04-13               North West    130
## 1517  2020-04-14               North West    130
## 1518  2020-04-15               North West    114
## 1519  2020-04-16               North West    135
## 1520  2020-04-17               North West     98
## 1521  2020-04-18               North West    114
## 1522  2020-04-19               North West     71
## 1523  2020-04-20               North West     83
## 1524  2020-04-21               North West     76
## 1525  2020-04-22               North West     87
## 1526  2020-04-23               North West     85
## 1527  2020-04-24               North West     67
## 1528  2020-04-25               North West     67
## 1529  2020-04-26               North West     55
## 1530  2020-04-27               North West     54
## 1531  2020-04-28               North West     57
## 1532  2020-04-29               North West     64
## 1533  2020-04-30               North West     60
## 1534  2020-05-01               North West     45
## 1535  2020-05-02               North West     56
## 1536  2020-05-03               North West     55
## 1537  2020-05-04               North West     48
## 1538  2020-05-05               North West     49
## 1539  2020-05-06               North West     44
## 1540  2020-05-07               North West     50
## 1541  2020-05-08               North West     43
## 1542  2020-05-09               North West     31
## 1543  2020-05-10               North West     42
## 1544  2020-05-11               North West     35
## 1545  2020-05-12               North West     38
## 1546  2020-05-13               North West     25
## 1547  2020-05-14               North West     26
## 1548  2020-05-15               North West     33
## 1549  2020-05-16               North West     32
## 1550  2020-05-17               North West     24
## 1551  2020-05-18               North West     31
## 1552  2020-05-19               North West     35
## 1553  2020-05-20               North West     27
## 1554  2020-05-21               North West     28
## 1555  2020-05-22               North West     26
## 1556  2020-05-23               North West     31
## 1557  2020-05-24               North West     26
## 1558  2020-05-25               North West     31
## 1559  2020-05-26               North West     27
## 1560  2020-05-27               North West     27
## 1561  2020-05-28               North West     28
## 1562  2020-05-29               North West     20
## 1563  2020-05-30               North West     19
## 1564  2020-05-31               North West     13
## 1565  2020-06-01               North West     12
## 1566  2020-06-02               North West     27
## 1567  2020-06-03               North West     22
## 1568  2020-06-04               North West     22
## 1569  2020-06-05               North West     16
## 1570  2020-06-06               North West     26
## 1571  2020-06-07               North West     20
## 1572  2020-06-08               North West     23
## 1573  2020-06-09               North West     17
## 1574  2020-06-10               North West     16
## 1575  2020-06-11               North West     16
## 1576  2020-06-12               North West     11
## 1577  2020-06-13               North West     10
## 1578  2020-06-14               North West     15
## 1579  2020-06-15               North West     16
## 1580  2020-06-16               North West     16
## 1581  2020-06-17               North West     13
## 1582  2020-06-18               North West     14
## 1583  2020-06-19               North West      7
## 1584  2020-06-20               North West     11
## 1585  2020-06-21               North West      8
## 1586  2020-06-22               North West     11
## 1587  2020-06-23               North West     13
## 1588  2020-06-24               North West     13
## 1589  2020-06-25               North West     15
## 1590  2020-06-26               North West      6
## 1591  2020-06-27               North West      7
## 1592  2020-06-28               North West      9
## 1593  2020-06-29               North West      9
## 1594  2020-06-30               North West      7
## 1595  2020-07-01               North West      3
## 1596  2020-07-02               North West      6
## 1597  2020-07-03               North West      7
## 1598  2020-07-04               North West      4
## 1599  2020-07-05               North West      6
## 1600  2020-07-06               North West      9
## 1601  2020-07-07               North West      8
## 1602  2020-07-08               North West      5
## 1603  2020-07-09               North West     10
## 1604  2020-07-10               North West      2
## 1605  2020-07-11               North West      5
## 1606  2020-07-12               North West      0
## 1607  2020-07-13               North West      6
## 1608  2020-07-14               North West      4
## 1609  2020-07-15               North West      5
## 1610  2020-07-16               North West      2
## 1611  2020-07-17               North West      4
## 1612  2020-07-18               North West      5
## 1613  2020-07-19               North West      3
## 1614  2020-07-20               North West      0
## 1615  2020-07-21               North West      2
## 1616  2020-07-22               North West      3
## 1617  2020-07-23               North West      3
## 1618  2020-07-24               North West      1
## 1619  2020-07-25               North West      1
## 1620  2020-07-26               North West      3
## 1621  2020-07-27               North West      1
## 1622  2020-07-28               North West      1
## 1623  2020-07-29               North West      2
## 1624  2020-07-30               North West      2
## 1625  2020-07-31               North West      0
## 1626  2020-08-01               North West      2
## 1627  2020-08-02               North West      1
## 1628  2020-08-03               North West      8
## 1629  2020-08-04               North West      3
## 1630  2020-08-05               North West      2
## 1631  2020-08-06               North West      2
## 1632  2020-08-07               North West      2
## 1633  2020-08-08               North West      2
## 1634  2020-08-09               North West      3
## 1635  2020-08-10               North West      2
## 1636  2020-08-11               North West      3
## 1637  2020-08-12               North West      0
## 1638  2020-08-13               North West      2
## 1639  2020-08-14               North West      2
## 1640  2020-08-15               North West      6
## 1641  2020-08-16               North West      2
## 1642  2020-08-17               North West      1
## 1643  2020-08-18               North West      2
## 1644  2020-08-19               North West      1
## 1645  2020-08-20               North West      1
## 1646  2020-08-21               North West      4
## 1647  2020-08-22               North West      3
## 1648  2020-08-23               North West      5
## 1649  2020-08-24               North West      4
## 1650  2020-08-25               North West      3
## 1651  2020-08-26               North West      4
## 1652  2020-08-27               North West      1
## 1653  2020-08-28               North West      2
## 1654  2020-08-29               North West      0
## 1655  2020-08-30               North West      2
## 1656  2020-08-31               North West      3
## 1657  2020-09-01               North West      0
## 1658  2020-09-02               North West      2
## 1659  2020-09-03               North West      1
## 1660  2020-09-04               North West      3
## 1661  2020-09-05               North West      6
## 1662  2020-09-06               North West      1
## 1663  2020-09-07               North West      8
## 1664  2020-09-08               North West      6
## 1665  2020-09-09               North West      5
## 1666  2020-09-10               North West      5
## 1667  2020-09-11               North West      1
## 1668  2020-09-12               North West      4
## 1669  2020-09-13               North West      2
## 1670  2020-09-14               North West      4
## 1671  2020-09-15               North West      4
## 1672  2020-09-16               North West      6
## 1673  2020-09-17               North West      7
## 1674  2020-09-18               North West      6
## 1675  2020-09-19               North West      3
## 1676  2020-09-20               North West      2
## 1677  2020-09-21               North West      2
## 1678  2020-09-22               North West      9
## 1679  2020-09-23               North West     14
## 1680  2020-09-24               North West     10
## 1681  2020-09-25               North West      8
## 1682  2020-09-26               North West     14
## 1683  2020-09-27               North West     11
## 1684  2020-09-28               North West     15
## 1685  2020-09-29               North West     12
## 1686  2020-09-30               North West     17
## 1687  2020-10-01               North West     17
## 1688  2020-10-02               North West     20
## 1689  2020-10-03               North West     15
## 1690  2020-10-04               North West     15
## 1691  2020-10-05               North West     15
## 1692  2020-10-06               North West     20
## 1693  2020-10-07               North West     20
## 1694  2020-10-08               North West     22
## 1695  2020-10-09               North West     24
## 1696  2020-10-10               North West     31
## 1697  2020-10-11               North West     31
## 1698  2020-10-12               North West     35
## 1699  2020-10-13               North West     26
## 1700  2020-10-14               North West     35
## 1701  2020-10-15               North West     36
## 1702  2020-10-16               North West     34
## 1703  2020-10-17               North West     52
## 1704  2020-10-18               North West     40
## 1705  2020-10-19               North West     43
## 1706  2020-10-20               North West     48
## 1707  2020-10-21               North West     51
## 1708  2020-10-22               North West     49
## 1709  2020-10-23               North West     50
## 1710  2020-10-24               North West     51
## 1711  2020-10-25               North West     63
## 1712  2020-10-26               North West     53
## 1713  2020-10-27               North West     49
## 1714  2020-10-28               North West     57
## 1715  2020-10-29               North West     74
## 1716  2020-10-30               North West     73
## 1717  2020-10-31               North West     63
## 1718  2020-11-01               North West     76
## 1719  2020-11-02               North West     65
## 1720  2020-11-03               North West     77
## 1721  2020-11-04               North West     64
## 1722  2020-11-05               North West     67
## 1723  2020-11-06               North West     76
## 1724  2020-11-07               North West     79
## 1725  2020-11-08               North West     83
## 1726  2020-11-09               North West     82
## 1727  2020-11-10               North West     68
## 1728  2020-11-11               North West     62
## 1729  2020-11-12               North West     64
## 1730  2020-11-13               North West     81
## 1731  2020-11-14               North West     61
## 1732  2020-11-15               North West     75
## 1733  2020-11-16               North West     74
## 1734  2020-11-17               North West     73
## 1735  2020-11-18               North West     71
## 1736  2020-11-19               North West     67
## 1737  2020-11-20               North West     52
## 1738  2020-11-21               North West     68
## 1739  2020-11-22               North West     52
## 1740  2020-11-23               North West     54
## 1741  2020-11-24               North West     64
## 1742  2020-11-25               North West     65
## 1743  2020-11-26               North West     53
## 1744  2020-11-27               North West     51
## 1745  2020-11-28               North West     46
## 1746  2020-11-29               North West     54
## 1747  2020-11-30               North West     48
## 1748  2020-12-01               North West     53
## 1749  2020-12-02               North West     48
## 1750  2020-12-03               North West     47
## 1751  2020-12-04               North West     48
## 1752  2020-12-05               North West     37
## 1753  2020-12-06               North West     43
## 1754  2020-12-07               North West     50
## 1755  2020-12-08               North West     49
## 1756  2020-12-09               North West     48
## 1757  2020-12-10               North West     49
## 1758  2020-12-11               North West     41
## 1759  2020-12-12               North West     48
## 1760  2020-12-13               North West     41
## 1761  2020-12-14               North West     51
## 1762  2020-12-15               North West     34
## 1763  2020-12-16               North West     41
## 1764  2020-12-17               North West     26
## 1765  2020-12-18               North West     47
## 1766  2020-12-19               North West     45
## 1767  2020-12-20               North West     37
## 1768  2020-12-21               North West     51
## 1769  2020-12-22               North West     52
## 1770  2020-12-23               North West     50
## 1771  2020-12-24               North West     58
## 1772  2020-12-25               North West     52
## 1773  2020-12-26               North West     56
## 1774  2020-12-27               North West     50
## 1775  2020-12-28               North West     48
## 1776  2020-12-29               North West     49
## 1777  2020-12-30               North West     49
## 1778  2020-12-31               North West     62
## 1779  2021-01-01               North West     54
## 1780  2021-01-02               North West     55
## 1781  2021-01-03               North West     57
## 1782  2021-01-04               North West     51
## 1783  2021-01-05               North West     56
## 1784  2021-01-06               North West     69
## 1785  2021-01-07               North West     61
## 1786  2021-01-08               North West     65
## 1787  2021-01-09               North West     69
## 1788  2021-01-10               North West     66
## 1789  2021-01-11               North West     79
## 1790  2021-01-12               North West     66
## 1791  2021-01-13               North West     85
## 1792  2021-01-14               North West     92
## 1793  2021-01-15               North West     87
## 1794  2021-01-16               North West     83
## 1795  2021-01-17               North West     81
## 1796  2021-01-18               North West     92
## 1797  2021-01-19               North West     92
## 1798  2021-01-20               North West     88
## 1799  2021-01-21               North West     85
## 1800  2021-01-22               North West    110
## 1801  2021-01-23               North West    103
## 1802  2021-01-24               North West     95
## 1803  2021-01-25               North West     86
## 1804  2021-01-26               North West    102
## 1805  2021-01-27               North West    104
## 1806  2021-01-28               North West    102
## 1807  2021-01-29               North West     99
## 1808  2021-01-30               North West     76
## 1809  2021-01-31               North West     85
## 1810  2021-02-01               North West     96
## 1811  2021-02-02               North West     82
## 1812  2021-02-03               North West     71
## 1813  2021-02-04               North West     79
## 1814  2021-02-05               North West     67
## 1815  2021-02-06               North West     62
## 1816  2021-02-07               North West     53
## 1817  2021-02-08               North West     73
## 1818  2021-02-09               North West     68
## 1819  2021-02-10               North West     71
## 1820  2021-02-11               North West     66
## 1821  2021-02-12               North West     67
## 1822  2021-02-13               North West     61
## 1823  2021-02-14               North West     50
## 1824  2021-02-15               North West     56
## 1825  2021-02-16               North West     53
## 1826  2021-02-17               North West     55
## 1827  2021-02-18               North West     51
## 1828  2021-02-19               North West     39
## 1829  2021-02-20               North West     32
## 1830  2021-02-21               North West     36
## 1831  2021-02-22               North West     25
## 1832  2021-02-23               North West     34
## 1833  2021-02-24               North West     34
## 1834  2021-02-25               North West     22
## 1835  2021-02-26               North West     37
## 1836  2021-02-27               North West     22
## 1837  2021-02-28               North West     28
## 1838  2021-03-01               North West     26
## 1839  2021-03-02               North West      5
## 1840  2021-03-03               North West      3
## 1841  2020-03-01               South East      0
## 1842  2020-03-02               South East      0
## 1843  2020-03-03               South East      1
## 1844  2020-03-04               South East      0
## 1845  2020-03-05               South East      1
## 1846  2020-03-06               South East      0
## 1847  2020-03-07               South East      0
## 1848  2020-03-08               South East      1
## 1849  2020-03-09               South East      1
## 1850  2020-03-10               South East      1
## 1851  2020-03-11               South East      1
## 1852  2020-03-12               South East      0
## 1853  2020-03-13               South East      1
## 1854  2020-03-14               South East      1
## 1855  2020-03-15               South East      5
## 1856  2020-03-16               South East      8
## 1857  2020-03-17               South East      7
## 1858  2020-03-18               South East     10
## 1859  2020-03-19               South East      9
## 1860  2020-03-20               South East     13
## 1861  2020-03-21               South East      7
## 1862  2020-03-22               South East     25
## 1863  2020-03-23               South East     20
## 1864  2020-03-24               South East     22
## 1865  2020-03-25               South East     29
## 1866  2020-03-26               South East     35
## 1867  2020-03-27               South East     36
## 1868  2020-03-28               South East     36
## 1869  2020-03-29               South East     55
## 1870  2020-03-30               South East     58
## 1871  2020-03-31               South East     65
## 1872  2020-04-01               South East     66
## 1873  2020-04-02               South East     55
## 1874  2020-04-03               South East     72
## 1875  2020-04-04               South East     80
## 1876  2020-04-05               South East     82
## 1877  2020-04-06               South East     88
## 1878  2020-04-07               South East    100
## 1879  2020-04-08               South East     83
## 1880  2020-04-09               South East    104
## 1881  2020-04-10               South East     88
## 1882  2020-04-11               South East     88
## 1883  2020-04-12               South East     88
## 1884  2020-04-13               South East     84
## 1885  2020-04-14               South East     65
## 1886  2020-04-15               South East     72
## 1887  2020-04-16               South East     56
## 1888  2020-04-17               South East     86
## 1889  2020-04-18               South East     57
## 1890  2020-04-19               South East     70
## 1891  2020-04-20               South East     87
## 1892  2020-04-21               South East     51
## 1893  2020-04-22               South East     54
## 1894  2020-04-23               South East     57
## 1895  2020-04-24               South East     64
## 1896  2020-04-25               South East     51
## 1897  2020-04-26               South East     51
## 1898  2020-04-27               South East     41
## 1899  2020-04-28               South East     40
## 1900  2020-04-29               South East     47
## 1901  2020-04-30               South East     29
## 1902  2020-05-01               South East     37
## 1903  2020-05-02               South East     36
## 1904  2020-05-03               South East     17
## 1905  2020-05-04               South East     35
## 1906  2020-05-05               South East     29
## 1907  2020-05-06               South East     25
## 1908  2020-05-07               South East     27
## 1909  2020-05-08               South East     26
## 1910  2020-05-09               South East     28
## 1911  2020-05-10               South East     19
## 1912  2020-05-11               South East     25
## 1913  2020-05-12               South East     27
## 1914  2020-05-13               South East     18
## 1915  2020-05-14               South East     32
## 1916  2020-05-15               South East     25
## 1917  2020-05-16               South East     22
## 1918  2020-05-17               South East     18
## 1919  2020-05-18               South East     23
## 1920  2020-05-19               South East     12
## 1921  2020-05-20               South East     22
## 1922  2020-05-21               South East     15
## 1923  2020-05-22               South East     17
## 1924  2020-05-23               South East     21
## 1925  2020-05-24               South East     17
## 1926  2020-05-25               South East     13
## 1927  2020-05-26               South East     19
## 1928  2020-05-27               South East     19
## 1929  2020-05-28               South East     12
## 1930  2020-05-29               South East     22
## 1931  2020-05-30               South East      8
## 1932  2020-05-31               South East     12
## 1933  2020-06-01               South East     11
## 1934  2020-06-02               South East     13
## 1935  2020-06-03               South East     18
## 1936  2020-06-04               South East     11
## 1937  2020-06-05               South East     11
## 1938  2020-06-06               South East     10
## 1939  2020-06-07               South East     12
## 1940  2020-06-08               South East      8
## 1941  2020-06-09               South East     11
## 1942  2020-06-10               South East     11
## 1943  2020-06-11               South East      5
## 1944  2020-06-12               South East      6
## 1945  2020-06-13               South East      7
## 1946  2020-06-14               South East      7
## 1947  2020-06-15               South East      8
## 1948  2020-06-16               South East     14
## 1949  2020-06-17               South East     10
## 1950  2020-06-18               South East      4
## 1951  2020-06-19               South East      7
## 1952  2020-06-20               South East      5
## 1953  2020-06-21               South East      3
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## 2462  2020-11-09               South West     12
## 2463  2020-11-10               South West      6
## 2464  2020-11-11               South West     13
## 2465  2020-11-12               South West     17
## 2466  2020-11-13               South West      9
## 2467  2020-11-14               South West      8
## 2468  2020-11-15               South West     16
## 2469  2020-11-16               South West     18
## 2470  2020-11-17               South West     17
## 2471  2020-11-18               South West     26
## 2472  2020-11-19               South West     15
## 2473  2020-11-20               South West     25
## 2474  2020-11-21               South West     25
## 2475  2020-11-22               South West     24
## 2476  2020-11-23               South West     14
## 2477  2020-11-24               South West     20
## 2478  2020-11-25               South West     25
## 2479  2020-11-26               South West     16
## 2480  2020-11-27               South West     21
## 2481  2020-11-28               South West     35
## 2482  2020-11-29               South West     15
## 2483  2020-11-30               South West     22
## 2484  2020-12-01               South West     19
## 2485  2020-12-02               South West     15
## 2486  2020-12-03               South West     14
## 2487  2020-12-04               South West     20
## 2488  2020-12-05               South West     17
## 2489  2020-12-06               South West     13
## 2490  2020-12-07               South West     16
## 2491  2020-12-08               South West     19
## 2492  2020-12-09               South West     22
## 2493  2020-12-10               South West     21
## 2494  2020-12-11               South West     20
## 2495  2020-12-12               South West     15
## 2496  2020-12-13               South West     19
## 2497  2020-12-14               South West     20
## 2498  2020-12-15               South West     20
## 2499  2020-12-16               South West      9
## 2500  2020-12-17               South West     26
## 2501  2020-12-18               South West     11
## 2502  2020-12-19               South West     22
## 2503  2020-12-20               South West     19
## 2504  2020-12-21               South West     22
## 2505  2020-12-22               South West     11
## 2506  2020-12-23               South West     16
## 2507  2020-12-24               South West     18
## 2508  2020-12-25               South West     19
## 2509  2020-12-26               South West     24
## 2510  2020-12-27               South West     24
## 2511  2020-12-28               South West     21
## 2512  2020-12-29               South West     20
## 2513  2020-12-30               South West     17
## 2514  2020-12-31               South West     27
## 2515  2021-01-01               South West     29
## 2516  2021-01-02               South West     24
## 2517  2021-01-03               South West     28
## 2518  2021-01-04               South West     31
## 2519  2021-01-05               South West     31
## 2520  2021-01-06               South West     27
## 2521  2021-01-07               South West     30
## 2522  2021-01-08               South West     34
## 2523  2021-01-09               South West     26
## 2524  2021-01-10               South West     34
## 2525  2021-01-11               South West     40
## 2526  2021-01-12               South West     48
## 2527  2021-01-13               South West     40
## 2528  2021-01-14               South West     36
## 2529  2021-01-15               South West     46
## 2530  2021-01-16               South West     56
## 2531  2021-01-17               South West     35
## 2532  2021-01-18               South West     46
## 2533  2021-01-19               South West     45
## 2534  2021-01-20               South West     64
## 2535  2021-01-21               South West     59
## 2536  2021-01-22               South West     60
## 2537  2021-01-23               South West     54
## 2538  2021-01-24               South West     59
## 2539  2021-01-25               South West     59
## 2540  2021-01-26               South West     46
## 2541  2021-01-27               South West     45
## 2542  2021-01-28               South West     51
## 2543  2021-01-29               South West     42
## 2544  2021-01-30               South West     39
## 2545  2021-01-31               South West     36
## 2546  2021-02-01               South West     28
## 2547  2021-02-02               South West     36
## 2548  2021-02-03               South West     31
## 2549  2021-02-04               South West     32
## 2550  2021-02-05               South West     24
## 2551  2021-02-06               South West     38
## 2552  2021-02-07               South West     35
## 2553  2021-02-08               South West     30
## 2554  2021-02-09               South West     30
## 2555  2021-02-10               South West     17
## 2556  2021-02-11               South West     19
## 2557  2021-02-12               South West     26
## 2558  2021-02-13               South West     27
## 2559  2021-02-14               South West     16
## 2560  2021-02-15               South West     19
## 2561  2021-02-16               South West     10
## 2562  2021-02-17               South West     18
## 2563  2021-02-18               South West     19
## 2564  2021-02-19               South West     18
## 2565  2021-02-20               South West     12
## 2566  2021-02-21               South West     16
## 2567  2021-02-22               South West     10
## 2568  2021-02-23               South West      6
## 2569  2021-02-24               South West      9
## 2570  2021-02-25               South West     12
## 2571  2021-02-26               South West      6
## 2572  2021-02-27               South West      6
## 2573  2021-02-28               South West     10
## 2574  2021-03-01               South West     13
## 2575  2021-03-02               South West      6
## 2576  2021-03-03               South West      1

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2021-03-04"

The completion date of the NHS Pathways data is Thursday 04 Mar 2021.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 15 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 15 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -18.956  -16.239   -5.478    6.492   33.052  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.205e+00  6.712e-02  77.548   <2e-16 ***
## note_lag    1.154e-05  1.254e-06   9.196   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 224.4256)
## 
##     Null deviance: 80888  on 314  degrees of freedom
## Residual deviance: 66884  on 313  degrees of freedom
##   (15 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  182.115503    1.000012
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 159.278995 207.234423
## note_lag      1.000009   1.000014

Rsq(lag_mod)
## [1] 0.1731319

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                             sysname 
##                                                                                            "Darwin" 
##                                                                                             release 
##                                                                                            "19.6.0" 
##                                                                                             version 
## "Darwin Kernel Version 19.6.0: Tue Jan 12 22:13:05 PST 2021; root:xnu-6153.141.16~1/RELEASE_X86_64" 
##                                                                                            nodename 
##                                                                           "Mac-1614938954273.local" 
##                                                                                             machine 
##                                                                                            "x86_64" 
##                                                                                               login 
##                                                                                              "root" 
##                                                                                                user 
##                                                                                            "runner" 
##                                                                                      effective_user 
##                                                                                            "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.4                         
## year           2021                        
## month          02                          
## day            15                          
## svn rev        80002                       
## language       R                           
## version.string R version 4.0.4 (2021-02-15)
## nickname       Lost Library Book

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.4 (2021-02-15)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.5     ggpubr_0.4.0         lubridate_1.7.10    
##  [4] chngpt_2020.10-12    cyphr_1.1.0          DT_0.17             
##  [7] kableExtra_1.3.4     janitor_2.1.0        remotes_2.2.0       
## [10] projections_0.5.2    earlyR_0.0.5         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.3      rio_0.5.26          
## [16] reshape2_1.4.4       rvest_0.3.6          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.1        stringr_1.4.0       
## [22] dplyr_1.0.4          purrr_0.3.4          readr_1.4.0         
## [25] tidyr_1.1.3          tibble_3.1.0         ggplot2_3.3.3       
## [28] tidyverse_1.3.0      here_1.0.1           reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] minqa_1.2.4       colorspace_2.0-0  selectr_0.4-2     ggsignif_0.6.1   
##  [5] ellipsis_0.3.1    rprojroot_2.0.2   snakecase_0.11.0  fs_1.5.0         
##  [9] rstudioapi_0.13   farver_2.1.0      fansi_0.4.2       splines_4.0.4    
## [13] knitr_1.31        jsonlite_1.7.2    nloptr_1.2.2.2    broom_0.7.5      
## [17] dbplyr_2.1.0      compiler_4.0.4    httr_1.4.2        backports_1.2.1  
## [21] assertthat_0.2.1  Matrix_1.3-2      cli_2.3.1         htmltools_0.5.1.1
## [25] tools_4.0.4       gtable_0.3.0      glue_1.4.2        Rcpp_1.0.6       
## [29] carData_3.0-4     cellranger_1.1.0  vctrs_0.3.6       svglite_2.0.0    
## [33] nlme_3.1-152      matchmaker_0.1.1  crosstalk_1.1.1   xfun_0.21        
## [37] ps_1.6.0          openxlsx_4.2.3    lme4_1.1-26       lifecycle_1.0.0  
## [41] statmod_1.4.35    rstatix_0.7.0     MASS_7.3-53       scales_1.1.1     
## [45] hms_1.0.0         parallel_4.0.4    sodium_1.1        yaml_2.2.1       
## [49] curl_4.3          gridExtra_2.3     stringi_1.5.3     highr_0.8        
## [53] kyotil_2020.10-12 boot_1.3-26       zip_2.1.1         rlang_0.4.10     
## [57] pkgconfig_2.0.3   systemfonts_1.0.1 evaluate_0.14     lattice_0.20-41  
## [61] labeling_0.4.2    htmlwidgets_1.5.3 cowplot_1.1.1     tidyselect_1.1.0 
## [65] plyr_1.8.6        magrittr_2.0.1    R6_2.5.0          generics_0.1.0   
## [69] DBI_1.1.1         mgcv_1.8-33       pillar_1.5.0      haven_2.3.1      
## [73] foreign_0.8-81    withr_2.4.1       survival_3.2-7    abind_1.4-5      
## [77] modelr_0.1.8      crayon_1.4.1      car_3.0-10        utf8_1.1.4       
## [81] rmarkdown_2.7     viridis_0.5.1     grid_4.0.4        readxl_1.3.1     
## [85] data.table_1.14.0 reprex_1.0.0      digest_0.6.27     webshot_0.5.2    
## [89] munsell_0.5.0     viridisLite_0.3.0